Critical exponents of the pair contact process with diffusion

TL;DR

This study uses Monte Carlo simulations to analyze the critical behavior of the pair contact process with diffusion, revealing critical exponents consistent with directed percolation and emphasizing the importance of finite-time corrections.

Contribution

The paper provides the first detailed estimate of critical exponents for the PCPD model, highlighting the relation to directed percolation and addressing slow convergence issues.

Findings

Critical exponents: δ ≈ 0.165 and β ≈ 0.31.

Density ratios converge to a constant at criticality.

Finite-time corrections are crucial for accurate exponent estimation.

Abstract

We study the pair contact process with diffusion (PCPD) using Monte Carlo simulations, and concentrate on the decay of the particle density $\rho$ with time, near its critical point, which is assumed to follow $\rho(t) \approx ct^{-\delta} +c_2t^{-\delta_2}+...$. This model is known for its slow convergence to the asymptotic critical behavior; we therefore pay particular attention to finite-time corrections. We find that at the critical point, the ratio of $\rho$ and the pair density $\rho_p$ converges to a constant, indicating that both densities decay with the same powerlaw. We show that under the assumption $\delta_2 \approx 2 \delta$, two of the critical exponents of the PCPD model are $\delta = 0.165(10)$ and $\beta = 0.31(4)$, consistent with those of the directed percolation (DP) model.